CBSE Class 12 Differential Equations — practice questions
35 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 Differential Equations in the app →The order of the differential equation $d^3y/dx^3 + (d^2y/dx^2)^2 + y = 0$ is:The general solution of $dy/dx = ky$ is:The integrating factor for $dy/dx + 2y = e^x$ is:A radioactive sample decays following $dN/dt = -\lambda N$. The amount $N(t)$ as a function of time is:The ORDER and DEGREE of the DE (d²y/dx²)³ + (dy/dx)⁵ + y = 0 are:The general solution of a 3rd-order DE contains how many arbitrary constants?The DE dy/dx = y/x is best solved by:For the linear DE dy/dx + (1/x)y = x, the INTEGRATING FACTOR μ(x) is:If a population grows exponentially as dN/dt = 0.1 N (with t in years), the DOUBLING TIME is:By Newton's law of cooling, a hot tea cup at 90°C in a room at 25°C cools so that:For the second-order LDE y'' − 5y' + 6y = 0, the auxiliary equation m² − 5m + 6 = 0 has roots m = 2, 3. The geA mass on a spring obeys d²x/dt² + ω²x = 0 (SHM). The period of oscillation is:Euler's method for a DE y' = f(x, y) computes the next value as:An equation involving derivatives of a dependent variable is a:An equation with derivatives in one independent variable only is:An equation with derivatives in several independent variables is:The order of a differential equation is the order of its:An equation whose highest derivative is the second has order:Degree can be defined only if the equation is a polynomial in:The degree is the highest power of the derivative that is:For an equation with a sine of a derivative, the degree is:A solution containing arbitrary constants is called the:A solution free from arbitrary constants is called:A particular solution comes from the general one by fixing the:The general solution of a differential equation is also called its:For a family of curves, the order equals the number of:A family of curves with two arbitrary constants gives an order of:A first order and first degree equation involves derivatives of order:Equations solvable by moving x and y to opposite sides use:Equations built from functions of the same degree throughout are:A differential equation states a relation between a function and its:The study at this stage is confined to equations that are:An equation whose highest derivative is the third has order:The power counted for the degree must be a whole number that is:Solutions of a differential equation form a set that is a: